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A281626
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a(n) = (sum of trivial divisors of n) - (sum of nontrivial divisors of n).
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1
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1, 3, 4, 3, 6, 2, 8, 3, 7, 4, 12, -2, 14, 6, 8, 3, 18, -1, 20, 0, 12, 10, 24, -10, 21, 12, 16, 2, 30, -10, 32, 3, 20, 16, 24, -17, 38, 18, 24, -8, 42, -10, 44, 6, 14, 22, 48, -26, 43, 9, 32, 8, 54, -10, 40, -6, 36, 28, 60, -46, 62, 30, 24, 3, 48, -10, 68, 12
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OFFSET
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1,2
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COMMENTS
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Trivial divisors of n are numbers 1 and n.
a(n) = 0 for numbers in A088831 (numbers n whose abundance is 2).
a(n) <= 0 for numbers in A005101 (abundant numbers).
a(n) > 0 for numbers in A263837 (non-abundant numbers).
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LINKS
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FORMULA
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a(1) = 1; for n>1, a(n) = (n+1) - (sigma(n) - n - 1) = 2*(n+1) - sigma(n) = n + 1 - A048050(n).
a(p) = p + 1 for p prime.
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EXAMPLE
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a(20) = (20+1) - (2+4+5+10) = 0.
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MATHEMATICA
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Table[If[n == 1, 1, 2 (n + 1) - DivisorSigma[1, n]], {n, 68}] (* Michael De Vlieger, Feb 11 2017 *)
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PROG
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(Magma) [1] cat [2*(n+1) - SumOfDivisors(n): n in [2..100]]
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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